Screwing spindles are known that have a linear actuator with a piston connected to a spindle shaft to rotate it. A method commonly used for controlling such spindles consists in subjecting the piston to differential tightening pressure, thereby generating the required torque for tightening the stopper on the neck of the package. A problem comes from the fact that when the stopper begins to be screwed on, there is little friction between the stopper and the neck, such that there is little opposition to rotation of the spindle. The spindle shaft thus acquires a high speed of rotation, and because of its inertia the spindle shaft stores a considerable amount of kinetic energy. The kinetic energy stored in this way causes the stopper to be tightened quickly until it comes into abutment, at which point the spindle shaft is caused to stop suddenly. On stopping, the stored kinetic energy is restored in the form of a dynamic torque which is applied to the stopper and which is greater than the required tightening torque. This dynamic torque can damage the stopper or the neck of the package, and it can make it necessary for a user of the package to have recourse to a tool for loosening the stopper.